In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

翻译：在本文中,我们研究了高顺序结构预测任务中的推论问题。在Markov随机字段中,高顺序推断任务的目标是最大限度地扩大标签空间的评分功能,分数功能可以分解成单级和高顺序潜力的总和。我们运用基因模型方法研究高顺序推论问题,并为准确标签回收提供两阶段的convex优化算法。我们还提供了与高端扩展有关的新高射结构属性,这在一般高顺序推论问题上是成功的。最后,我们用新的高压切格型不平等将算法的性能与高端扩展属性联系起来。